By the uniqueness statement from Theorem REF , we conclude that \(\frac{\partial }{\partial \tau _0}\)  is the vector field \(\sf R\)  restricted to the locus \(\sf L_{op}\) . If we consider the coordinate \(q = e^{2\pi i\tau _0}\) , then \(\sf R\)  becomes \(2\pi i q\frac{\partial }{\partial q}\) . Writing the functions \(\sf F\)  and \(\sf Y\)  (or \(\frac{d\tau _5}{d\tau _0}\)  and \(\frac{d\tau _3}{d\tau _0}\) , respectively) in the coordinate \(q\)  gives us virtual counts of disks with boundary on the real quintic and virtual counts of rational curves on a quintic threefold. Looking at the expressions of the \(\tau _i\)  in terms of \(x_{ij}\)  we get, for example, that \(\tau _4\)  is given by \(\frac{x_{01}}{x_{21}}\) , i.e., the quotient of a solution for the non homogenous Picard-Fuchs equation by the holomorphic solution to the homogenous equation. By using the \(A\)  model correlation function in [1]}, the expression of \(\tau _4\)  in terms of \(\tau _0\)  is
\(\tau _4 =\frac{\tau _0}{2} + \frac{1}{4}+\frac{1}{2 \pi ^{2}} \frac{5^4}{(2\pi i)^3}\sum _{d \text{ odd }} N_{d}e^{d\pi i\tau _0 },\) 
